Probably the most celebrated place in Matsuyama, on Shikoku’s northwest coast, is Dogo Onsen, a collection of public baths somewhat reminiscent of the bathhouse complex for spirits in Hayao Miyazaki’s Oscar-winning anime film, Spirited Away.

St. Hilaire and Neal last week in Tribeca—Mr. Matsuyama, who at 26 is a year older than his band mates, was out of town—they said that since all three members sing, they had a natural appreciation for melody.